The invention is based on a fuel injection pump for internal combustion engines. Such a fuel injection pump is known from U.S. Pat. No. 4,830,587. There, both the onset and end of supply are regulated via an annular slide that is displaceable on the pump piston; one face edge of the annular slide controls the supply onset as the control recess of the pump piston enters the annular slide, and along with the control edge of the oblique groove oriented toward the pump work chamber, a radial control bore disposed in the annular slide controls the end of supply. Particularly in fuel injection pumps that operate at high injection pressure, upon closing and opening of the control bores, voids in the fuel (vapor bubbles) form as the fuel flows out of the pump work chamber into the suction chamber of the fuel injection pump surrounding the control slide; because of the inertia of the fuel, these voids cause areas of negative pressure in the fuel flow, and at the moment that happens, the fuel pressure drops below the vapor pressure. Some of the vapor bubbles are reaspirated into the control bores from the fuel injection pump suction chamber during the intake stroke of the pump piston. They are entrained by the flow and implode upon contact with a solid wall. As a result, a spike of liquid at maximum energy (high-charge effect) briefly forms, which can remove material from the wall and cause subsequent damage (cavitation) to the fuel injection pump. Avoiding or limiting the aforementioned cavitation damage is thus a necessity, for the sake of safe operation over the full service life of even fuel injection pumps that operate at a very high fuel pressure.